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Physics-

General

Easy

Question

A block of mass M on a horizontal smooth surface is pulled by a load of mass M /2 by means of a rope AB and string BC as shown in the figure. The length & mass of the rope AB are L and M /2 respectively. As the block is pulled from AB = L to AB = 0 its acceleration changes from

$\frac{3 g}{4} tog$
$\frac{g}{4} to \frac{g}{2}$
$\frac{g}{4} to g$
$\frac{3 g}{2} to 2 g$

The correct answer is: $fraction numerator g over denominator 4 end fraction text to end text fraction numerator g over denominator 2 end fraction$

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The diagram to the right shows the velocity-time graph for two masses R and S that collided elastically. Which of the following statements is true? (I) R and S moved in the same direction after the collision. (II) Kinetic energy of the system (R & S) is minimum at t = 2 milli sec. (III) The mass of R was greater than mass of S.

The diagram to the right shows the velocity-time graph for two masses R and S that collided elastically. Which of the following statements is true? (I) R and S moved in the same direction after the collision. (II) Kinetic energy of the system (R & S) is minimum at t = 2 milli sec. (III) The mass of R was greater than mass of S.

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Two massless string of length 5 m hang from the ceiling very near to each other as shown in the figure. Two balls A and B of masses 0.25 kg and 0.5 kg are attached to the string. The ball A is released from rest at a height 0.45 m as shown in the figure. The collision between two balls is completely elastic. Immediately after the collision, the kinetic energy of ball B is 1 J. The velocity of ball A just after the collision is

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The system of the wedge and the block connected by a massless spring as shown in the figure is released with the spring in its natural length. Friction is absent. maximum elongation in the spring will be

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physics-General

The position vector of a point P is $bold r with rightwards arrow on top equals x ı with not stretchy hat on top plus y ȷ with not stretchy hat on top plus z k with not stretchy hat on top$ where $straight x comma straight y comma straight z element of straight N$ and $times a with not stretchy bar on top equals ı with not stretchy hat on top plus 2 ȷ with not stretchy hat on top plus k with not stretchy hat on top times ∣ f times r with not stretchy rightwards arrow on top times a with not stretchy rightwards arrow on top equals 20$ . If , the number of possible position of P is

The position vector of a point P is $bold r with rightwards arrow on top equals x ı with not stretchy hat on top plus y ȷ with not stretchy hat on top plus z k with not stretchy hat on top$ where $straight x comma straight y comma straight z element of straight N$ and $times a with not stretchy bar on top equals ı with not stretchy hat on top plus 2 ȷ with not stretchy hat on top plus k with not stretchy hat on top times ∣ f times r with not stretchy rightwards arrow on top times a with not stretchy rightwards arrow on top equals 20$ . If , the number of possible position of P is

parallel

$text Let end text f left parenthesis x right parenthesis equals x plus s i n invisible function application x text and end text g left parenthesis x right parenthesis text be the inverse of end text f left parenthesis x right parenthesis text . Then area bounded by end text g left parenthesis x right parenthesis text and end text text the ordinates end text x equals 0 comma x equals pi text is end text$

$text Let end text f left parenthesis x right parenthesis equals x plus s i n invisible function application x text and end text g left parenthesis x right parenthesis text be the inverse of end text f left parenthesis x right parenthesis text . Then area bounded by end text g left parenthesis x right parenthesis text and end text text the ordinates end text x equals 0 comma x equals pi text is end text$

A function f is continuous on the interval $left square bracket 0 comma pi right square bracket. text If end text I subscript 1 end subscript equals stretchy integral subscript 0 end subscript superscript pi end superscript f left parenthesis s i n invisible function application x right parenthesis d x text and end text I subscript 2 end subscript equals stretchy integral subscript 0 end subscript superscript pi end superscript x f left parenthesis s i n invisible function application x right parenthesis d x$ then evaluate ratio $fraction numerator I subscript 2 end subscript over denominator I subscript 1 end subscript end fraction$

A function f is continuous on the interval $left square bracket 0 comma pi right square bracket. text If end text I subscript 1 end subscript equals stretchy integral subscript 0 end subscript superscript pi end superscript f left parenthesis s i n invisible function application x right parenthesis d x text and end text I subscript 2 end subscript equals stretchy integral subscript 0 end subscript superscript pi end superscript x f left parenthesis s i n invisible function application x right parenthesis d x$ then evaluate ratio $fraction numerator I subscript 2 end subscript over denominator I subscript 1 end subscript end fraction$

Suppose A and B are two nonsingular matrices such that $A B equals B A to the power of 2 end exponent text and end text B to the power of 5 end exponent equals I comma text then end text$

Suppose A and B are two nonsingular matrices such that $A B equals B A to the power of 2 end exponent text and end text B to the power of 5 end exponent equals I comma text then end text$

parallel

If A is the area between the curve $y equals x to the power of 6 end exponent left parenthesis 1 minus x right parenthesis to the power of 7 end exponent$ and x - axis then the number of prime factors of A $blank to the power of negative 1 end exponent text is end text$

If A is the area between the curve $y equals x to the power of 6 end exponent left parenthesis 1 minus x right parenthesis to the power of 7 end exponent$ and x - axis then the number of prime factors of A $blank to the power of negative 1 end exponent text is end text$

$stretchy integral subscript 0 end subscript superscript pi end superscript fraction numerator d x over denominator left parenthesis 5 plus 4 c o s invisible function application x right parenthesis to the power of 2 end exponent end fraction equals$

$stretchy integral subscript 0 end subscript superscript pi end superscript fraction numerator d x over denominator left parenthesis 5 plus 4 c o s invisible function application x right parenthesis to the power of 2 end exponent end fraction equals$

The value of the definite Integral $text . end text stretchy integral subscript negative 2008 end subscript superscript 2008 end superscript fraction numerator f to the power of ´ end exponent left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis negative x right parenthesis over denominator left parenthesis 2008 right parenthesis to the power of x end exponent plus 1 end fraction d x text equals end text$

The value of the definite Integral $text . end text stretchy integral subscript negative 2008 end subscript superscript 2008 end superscript fraction numerator f to the power of ´ end exponent left parenthesis x right parenthesis plus f to the power of ´ end exponent left parenthesis negative x right parenthesis over denominator left parenthesis 2008 right parenthesis to the power of x end exponent plus 1 end fraction d x text equals end text$

parallel

The integral $integral s i n invisible function application 2 x open parentheses 1 minus fraction numerator 3 over denominator 2 end fraction c o s invisible function application x close parentheses e to the power of s i n to the power of 2 end exponent invisible function application x plus c o s to the power of 3 end exponent invisible function application x end exponent d x text end text$ is equal to

The integral $integral s i n invisible function application 2 x open parentheses 1 minus fraction numerator 3 over denominator 2 end fraction c o s invisible function application x close parentheses e to the power of s i n to the power of 2 end exponent invisible function application x plus c o s to the power of 3 end exponent invisible function application x end exponent d x text end text$ is equal to

A point P moves in xy – plane in such a way that $left square bracket vertical line x vertical line right square bracket plus left square bracket vertical line y vertical line right square bracket equals 1 comma text where end text left square bracket. right square bracket$ denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to

A point P moves in xy – plane in such a way that $left square bracket vertical line x vertical line right square bracket plus left square bracket vertical line y vertical line right square bracket equals 1 comma text where end text left square bracket. right square bracket$ denotes the greatest integer function. Area of the region representing all possible positions of the point P is equal to

The value of $stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text$

The value of $stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text$

parallel

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